Figure REF (a) shows comparisons between numerical and analytical solutions for the height
\(H_{r} = u_{+} + a_{r}\)  of the resonant wavetrain. There is again excellent agreement, as expected as the WKB solution was
previously found to be in excellent agreement with numerical solutions [1]}. It can be seen that as the
RDSW regime is approached the amplitude \(a_{r} = H_{r} - u_{+}\)  of the resonant wavetrain goes to zero, as required. As
discussed in Section  the resonant wavetrain in the CDSW regime is unstable when its amplitude is low and
stabilises at high enough amplitude. For the comparisons of Figure REF (a) the amplitudes and heights of
low amplitude numerical resonant waves were determined before instability broke the wavetrain up. In this regard, a unit
distance in the non-dimensional variable \(z\)  corresponds to about \(2\mu m\)  for optical beams in the near infrared
[2]}, [3]}, [4]}. Typical experimental nematic cell lengths are \(\sim 1mm\) , which is \(z=500\) . As
shown in Figure REF  the breakup of the resonant wavetrain in the vicinity of the CDSW occurs after \(z=1000\) .
This is well beyond the experimental distance at which optical solitary waves can be observed, due to their decay due to
scattering losses [5]}, [6]}. Numerical solutions show that the mean height of the resonant wavetrain is given by \(\bar{u}_{r} = \sqrt{q\theta _{r}}\) . The resonant wavetrain is rapidly varying. Averaging the director equation () then gives this mean height expression. Figure REF (b) shows a comparison between the mean height \(\bar{u}_{r}\)  of
the resonant wavetrain as given by numerical solutions and by the theoretical CDSW value \(\bar{u}_{r}=u_{+}\) , with
excellent agreement seen. Finally, Figure REF (c) shows comparisons for the wavenumber \(k_{r}\)  of the resonant
wavetrain. The numerical values of \(k_{r}\)  were determined by averaging over the resonant wavetrain. Unlike the resonant
wave height and mean level, the comparison is poor, except near the TDSW regime where the resonant wavetrain restabilises. The
reason is that the resonant wavetrain is unstable over nearly all of the CDSW regime and does not
consist of a single dominant wavenumber, as seen in Figures REF  and REF .
